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(libc.info)FP Exceptions

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FP Exceptions
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   The IEEE 754 standard defines five "exceptions" that can occur
during a calculation.  Each corresponds to a particular sort of error,
such as overflow.

   When exceptions occur (when exceptions are "raised", in the language
of the standard), one of two things can happen.  By default the
exception is simply noted in the floating-point "status word", and the
program continues as if nothing had happened.  The operation produces a
default value, which depends on the exception (see the table below).
Your program can check the status word to find out which exceptions
happened.

   Alternatively, you can enable "traps" for exceptions.  In that case,
when an exception is raised, your program will receive the `SIGFPE'
signal.  The default action for this signal is to terminate the
program.  Note: Signal Handling, for how you can change the effect of
the signal.

   In the System V math library, the user-defined function `matherr' is
called when certain exceptions occur inside math library functions.
However, the Unix98 standard deprecates this interface.  We support it
for historical compatibility, but recommend that you do not use it in
new programs.

The exceptions defined in IEEE 754 are:

`Invalid Operation'
     This exception is raised if the given operands are invalid for the
     operation to be performed.  Examples are (see IEEE 754, section 7):
       1. Addition or subtraction: oo - oo.  (But oo + oo = oo).

       2. Multiplication: 0 * oo.

       3. Division: 0/0 or oo/oo.

       4. Remainder: x REM y, where y is zero or x is infinite.

       5. Square root if the operand is less then zero.  More
          generally, any mathematical function evaluated outside its
          domain produces this exception.

       6. Conversion of a floating-point number to an integer or decimal
          string, when the number cannot be represented in the target
          format (due to overflow, infinity, or NaN).

       7. Conversion of an unrecognizable input string.

       8. Comparison via predicates involving < or >, when one or other
          of the operands is NaN.  You can prevent this exception by
          using the unordered comparison functions instead; see Note:
          FP Comparison Functions.

     If the exception does not trap, the result of the operation is NaN.

`Division by Zero'
     This exception is raised when a finite nonzero number is divided
     by zero.  If no trap occurs the result is either +oo or -oo,
     depending on the signs of the operands.

`Overflow'
     This exception is raised whenever the result cannot be represented
     as a finite value in the precision format of the destination.  If
     no trap occurs the result depends on the sign of the intermediate
     result and the current rounding mode (IEEE 754, section 7.3):
       1. Round to nearest carries all overflows to oo with the sign of
          the intermediate result.

       2. Round toward 0 carries all overflows to the largest
          representable finite number with the sign of the intermediate
          result.

       3. Round toward -oo carries positive overflows to the largest
          representable finite number and negative overflows to -oo.

       4. Round toward oo carries negative overflows to the most
          negative representable finite number and positive overflows
          to oo.

     Whenever the overflow exception is raised, the inexact exception
     is also raised.

`Underflow'
     The underflow exception is raised when an intermediate result is
     too small to be calculated accurately, or if the operation's
     result rounded to the destination precision is too small to be
     normalized.

     When no trap is installed for the underflow exception, underflow is
     signaled (via the underflow flag) only when both tininess and loss
     of accuracy have been detected.  If no trap handler is installed
     the operation continues with an imprecise small value, or zero if
     the destination precision cannot hold the small exact result.

`Inexact'
     This exception is signalled if a rounded result is not exact (such
     as when calculating the square root of two) or a result overflows
     without an overflow trap.